Bayesian networks often are used in the process of determining probability distribution functions in multi-variable universes. One particular application in which Bayesian networks are commonly used to generate distributions that follow probability density functions is in localization techniques for mobile wireless devices.
Particularly, in wireless communication environments such as IEEE 802.11b or 802.11g wireless LANs, it is often a desirable feature to determine the location of a mobile wireless device using the network based on the characteristics of signals from the mobile wireless device received at multiple antennas of the wireless network (or vice versa). The characteristics are ones that are indicative of the location of the device relative to the landmarks. For instance, received signal strength (e.g., RSSI) or signal-to-noise ratio (S/N) are indicative of the distance between the landmark and the mobile device. On the other hand, using directional antennas, the angle of arrival of the signal can be used as an indicator of the bearing of the mobile device relative to the landmark.
The localization can be determined either by the devices themselves or by the network. That is, in some localization systems, the network determines the location of the wireless devices based on data collected by the landmarks and transmitted through the network to a central processing unit that determines the location of the devices. However, in other wireless device location systems, the wireless devices themselves may measure the characteristics of signals received from the landmarks to determine their own locations. In some applications of the latter type, the mobile wireless device may then transmit its own location to the network for use by other network equipment. In other applications, however, the mobile wireless device may be the only equipment that needs to know its location, such that the location as determined by the mobile wireless device need not be transmitted to any other equipment at all.
In order to simplify the following discussion, the following discussion shall speak in terms of an exemplary wireless network localization system in which the landmarks measure signal characteristics of signals transmitted from the mobile wireless devices as received at multiple landmarks of the network to determine the locations of the mobile wireless devices. However, the relevant principles would be equally applicable to localization systems using the inverse operational paradigm noted above.
There are any number of practical applications for such mobile wireless device localization. For instance, in hospitals and manufacturing plants, it may be desirable to track down the location of an individual or a piece of equipment using such a technique. The individual can be equipped with a wireless device (which may simply be the individual's personal cell phone) that communicates with the wireless LAN. The person can be located by locating the wireless device (assuming, obviously, that the person is carrying the wireless device on his or her person). Additionally, portable equipment can be equipped with a wireless transmitter and/or transceiver so that it can be located using such localization techniques.
Several different techniques are available for mobile wireless device localization. These techniques generally involve the gathering of information about one or more characteristics of the signals received from the wireless devices at a plurality of landmarks in the wireless network environment (or alternately signals received at the mobile wireless devices from a plurality of network landmarks). A landmark generally is a stationary wireless transmitter, receiver, or transceiver having a known location and that can communicate with the mobile wireless devices. Thus, for instance, landmarks typically include network base stations and other fixed position network nodes. These types of landmarks usually have both wireless and wired capabilities so that they can serve as a connection point between the wireless portion of a network and the wired portion of the network. However, alternately, a landmark need not be a communication node of the network. A landmark can be placed in the area covered by the wireless network strictly as a transmitter or receiver strictly for the purpose of providing a network landmark for use in localization of mobile wireless devices.
There are many different general techniques for wireless device localization, including triangulation, trilateration, and scene-matching.
In scene-matching, for instance, one first builds a map of the wireless network by placing a wireless device at multiple locations in the wireless network environment and recording signal characteristics of signals transmitted by the device as received at multiple landmarks for each such location to build a scene map of signal characteristics as a function of location. Once a scene map is built and stored, an algorithm tries to match the signal characteristics of each wireless device to the location in the scene map that most closely corresponds to those signal characteristics.
On the other hand, in systems that utilize triangulation, the landmarks use directional antennas so that they can measure the angle of arrival of signals at the landmarks to determine the relative bearing between the wireless device and each of the landmarks. By correlating the bearing data of multiple landmarks, the location of the device can be predicted by relatively simple trigonometric algorithms.
In lateration, signal characteristics such as RSSI and/or S/N of signals received from a wireless device at a plurality of landmarks are used as an indication of the distance between the wireless device and the various landmarks. Time of Flight is another characteristic that can be determined and used as an indication of distance. Given the distance between the wireless device and a plurality of different landmarks, the location of the device can be predicted by lateration equations. (Note the use of the term lateration, rather than the more common term trilateration in order to avoid any implication that there must be three and only three reference points (or landmarks).
If RSSI or S/N were closely correlated to the distance between a wireless device and a landmark, then making a fairly reliable prediction of the location of wireless devices would be a computationally simple task. However, that is not the case in the real world. Both RSSI and S/N are affected by many factors in addition to the distance between the device and a landmark. For instance, RSSI and S/N are dependent on the number of walls or other obstacles between the two devices, the relative humidity, interference with other RF devices, etc.
All of these variables, including distance, are unknown and it is practically impossible to develop a closed equation set to solve for location in a real-world environment. Accordingly, such problems are commonly solved using predictive statistical methods such as Bayesian networks using Markov Chain Monte Carlo and other such simulations, which are well known statistical modeling techniques.
Bayesian networks and Markov Chain Monte Carlo simulations are well known in the field of statistics and, in fact, are already being used in mobile wireless device localization systems. However, as the number of dimensions in the network (i.e., the number of unknown variables that must be solved for) increases, the computational load can very quickly exceed reasonable signal processing capabilities. For instance, Markov Chain Monte Carlo simulations involve the collection of many “samples”, wherein each sample comprises one specific value assigned to each of the variables. In a typical mobile wireless device localization system, there likely will be at least five variables, including some or all of X coordinate, Y coordinate, Z coordinate, and at least two or three distinct signal propagation constants. With five or more dimensions, the computational load necessary to generate a probability density function using Bayesian networks and Markov Chain Monte Carlo simulations is significant and difficult to perform in real time using the hardware and software that is practically available.
It would be desirable to reduce the processing load to perform mobile wireless device localization.
It also would be desirable in general to simplify the use of Bayesian networks and Markov Chain Monte Carlo simulations in statistical analysis.